FaradayAnalytics

Advanced Numerical Solutions

Advanced numerical methods · HPC-grade tooling

Scientific computing,
from prototype notebooks to production-grade solvers.

FaradayAnalytics designs, optimizes, and deploys numerical algorithms for PDEs, large-scale optimization, Monte Carlo simulation, and data-driven models—bridging the gap between mathematical theory and high-performance software.

Start a project → Explore capabilities

Nonlinear PDE Solver Finite elements · Newton–Krylov · MPI

Converged in 7 iterations

Δt = 1e-3

Sparse stiffness matrix (A)

3.9e+3

-2.1e+2

4.2e+3

-2.0e+2

4.1e+3

-2.0e+2

3.8e+3

Residual norm vs iteration

Newton–Krylov

Preconditioned

Tolerance

Core capabilities

We combine rigorous numerical analysis with modern engineering practices— from Python prototyping to C++ and GPU-accelerated implementations.

PDE & continuum simulation

Design and implementation of robust solvers for elliptic, parabolic, and hyperbolic PDEs using finite difference, finite element, or finite volume schemes.

FEM / FVM Multigrid Adaptive time-stepping

Large-scale optimization

Numerical optimization for inverse problems, calibration, and control: gradient-based and derivative-free methods on CPU & GPU.

Quasi-Newton AD-enabled Constrained solvers

Uncertainty & Monte Carlo

High-throughput Monte Carlo, variance reduction, and surrogate-based UQ for risk analysis and sensitivity studies.

MCMC Surrogates Sobol indices

High-performance computing

Parallelization (MPI, OpenMP, CUDA) and performance tuning for existing simulation codes and workflows.

MPI / distributed GPU offload Profiling & tuning

Data-driven numerical models

Hybrid ML + physics workflows—PINNs, reduced-order models, and system identification anchored in domain equations.

PINNs ROMs Operator learning

End-to-end consulting

From feasibility studies and algorithm selection to production deployment and documentation for your team.

Tech due diligence Code review Training

Where we add the most value

FaradayAnalytics works with engineering and research teams that already have strong domain expertise and need numerical reliability, performance, and clarity.

When prototypes won't scale You have working notebooks or scripts, but runtimes explode or numerical artifacts appear at realistic problem sizes.
When physics and data need to agree You want models that respect governing equations while integrating empirical data and modern machine learning.
When decisions depend on accuracy Regulatory, safety, or financial decisions hinge on quantified uncertainty and well-behaved numerical schemes.

Computational engineering Structural mechanics, fluid flow, heat transfer, and multi-physics coupling across time and length scales.
Energy & climate modeling Power systems, grid simulation, subsurface flow, and climate-impact scenario analysis.
Quantitative finance & risk PDE-based pricing, stochastic differential equations, and Monte Carlo engines tuned for latency and throughput.
R&D and applied science Support for internal research groups that need an implementation partner for complex numerical ideas.

Talk to FaradayAnalytics

Share a brief about your numerical challenge

Describe your equations, data, and constraints. We typically respond with an initial technical assessment and potential solution paths within a few business days.

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